JPWO2008081932A1 - Finite automaton generation system for character string matching, generation method thereof, and generation program - Google Patents

Abstract

The present invention provides a system, method, and program that enable conversion to a finite automaton that describes a transition condition with an arbitrary number of characters without increasing the number of states of the finite automaton for one character transition. The NFA conversion means 21 receives the number of characters simultaneously processed in parallel from the input device 1, and is stored in the NFA conversion matrix storage unit 32 and the one-character transition finite automaton description matrix stored in the NFA description matrix storage unit 31. Using the description matrix that is the result of the conversion in the middle, conversion processing is performed to a finite automaton having a transition condition with the number of characters processed in parallel. The NFA conversion means 21 stores the results in the NFA conversion result matrix storage unit 32 sequentially. When the conversion is completed, the result output means 22 reads the resulting NFA description matrix from the NFA conversion result matrix storage unit 32 and outputs it to the output device 4.

Description

[Description of related applications]
The present invention is based on the priority claim of Japanese patent application: Japanese Patent Application No. 2006-355533 (filed on Dec. 28, 2006), the entire contents of which are incorporated herein by reference. It shall be.

  The present invention relates to a finite automaton generation technique for character string collation, and more particularly to a finite automaton generation system, method, and generation program for character string collation that can perform character string collation by simultaneous parallel input of a plurality of character strings.

  Conventionally, a non-deterministic finite automaton (NFA) that allows a plurality of transition destinations for the same character from one state is used as a finite automaton for character string matching (pattern matching). There is a method or a method using a deterministic finite automaton (DFA) that does not allow it.

  For example, as described in Patent Literature 1 and Non-Patent Literature 1, the NFA can construct a syntax tree from search target conditions such as a given regular expression and generate the syntax tree based on the syntax tree. The DFA can be generated using NFA.

  In general, in pattern matching processing in software, states such as NFA and DFA are stored in a memory, and each time the state transitions, pattern matching is performed while extracting information about the state from the memory. At this time, since there are a plurality of states as transition destinations from a certain state to a certain input character in NFA, it is not possible to determine to which state a correct result can be obtained. In the case of failure, a process of transitioning to another state using the backtracking method is required when it fails.

  On the other hand, DFA has only one transition destination for a certain input character from a certain state, so that there is an advantage that processing can be performed at a speed higher than that of NFA. There is a disadvantage that capacity is required.

  In order to solve the problem of pattern matching processing in such software, in recent years, there is a method of performing high-speed pattern matching using NFA by taking advantage of high speed due to the parallel operation by directly incorporating NFA into a hardware circuit (non- Patent Document 2). There is also a method that aims to further improve the search throughput by increasing the number of input characters in one clock cycle (Non-patent Document 3). Furthermore, a method for improving the search throughput by inputting a character string of a plurality of characters at the same time by performing an NFA state transition condition with a plurality of characters has been proposed (Non-patent Documents 4 and 5). .

JP 2003-242179A (paragraph 20-34, FIGS. 1 to 9) Algorithm and data structure for C-programmers (pages 297-330, Yoshiyuki Kondo, 1998) Proceedings of the 9th Annual IEEE Symposium on Field-Programmable Custom Computing Machines (pp. 227-238, Reetinder Sidhu, Viktor K. Prasanna, 2001) Proceedings of 2004 IEEE International Conference on Field-Programmable Technology (pages 25-32, Peter Sutton, 2004) Proceedings of the 12th Annual IEEE Symposium on Field-Programmable Custom Computing Machines (Pages 249-257, Christopher R. Clark, David E. Schimmel, 2004) IPSJ Transactions: Computing System Vol.46, No.SIG12 (ACS11) (Pages 120-128, Toshihiro Katashita, Junji Maeda, Masato Ono, Kenji Toda, Yoshinori Yamaguchi, 2005)

  The disclosures of Patent Document 1 and Non-Patent Documents 1 to 5 are incorporated herein by reference. The following is an analysis of the related art according to the present invention. As described above, the method of performing pattern matching by directly incorporating NFA into hardware has the following problems.

  The first problem is that the search throughput cannot be further improved only by incorporating an NFA generated from a regular expression or the like.

  The reason is that since the state transition condition of the incorporated NFA is a condition for one input character of the character string to be searched, only one character can be searched per clock cycle.

  The second problem is that merely increasing the number of search characters per clock cycle without changing the NFA of one character transition as described above does not directly lead to an improvement in search throughput.

  The reason is that simply increasing the number of search characters per clock cycle increases the path by the number of characters to be processed at the same time, increasing the cycle of the clock cycle and consequently lowering the operating frequency. It is. In other words, even if the number of characters is quadrupled, there is a possibility that the operating frequency will be 1/4 or less.

  The third problem is that a flexible character string search like a regular expression cannot be performed by the current method in which the state transition condition of NFA is performed by a plurality of characters.

  The reason is not an NFA that includes a loop composed of regular expressions, but only a simple character string search (exact match) that expands the loop and eliminates the loop is considered.

  The fourth problem is that the number of states increases when the NFA state transition condition is extended to a plurality of characters.

  The reason is that NFA is generated for the number of characters to be processed in consideration of the offset in the number of characters to be processed simultaneously.

  Accordingly, a first problem to be solved by the present invention is to provide a finite automaton generation system, a generation method, and a generation program for performing flexible character string search using a regular expression or the like at high speed.

  Furthermore, a second problem to be solved by the present invention is a system and a generation method for generating a search target that can construct an NFA that transitions by one character into a finite automaton that matches an arbitrary number of characters for simultaneous parallel processing. And providing a generation program.

  Furthermore, a third problem to be solved by the present invention is a system, a generation method, and a generation method for generating a finite automaton that matches the number of characters for which parallel processing is performed without increasing the number of NFA states that transition by one character. To provide a program.

  According to the present invention, there is provided a finite automaton generation system (method, program) that increases the number of characters in a transition condition of a finite automaton composed of transition conditions of a fixed number of characters to an arbitrarily designated number of characters. The finite automaton is described in a matrix format. In the present invention, the increasing means does not change the number of states of the original finite automaton. Alternatively, in the present invention, the increasing means follows a matrix operation having a predefined operation rule. Alternatively, in the present invention, the increasing means applies a predetermined calculation rule to a matrix calculation using a plurality of partial matrices. In the present invention, the matrix calculation using the plurality of partial matrices generates and uses a partial matrix every time the calculation is performed. Alternatively, in the present invention, the matrix calculation using the plurality of partial matrices may be performed by generating a partial matrix in advance and using the partial matrix.

The finite automaton generation system according to the first aspect of the present invention includes an NFA description matrix storage unit (31 in FIG. 1) that stores in advance a matrix describing an NFA of one character transition, and an NFA description matrix of one character transition. Alternatively, the NFA description matrix of the p-character transition is read from the NFA description matrix storage unit (31 in FIG. 1) or the NFA conversion result matrix storage unit (32 in FIG. 1) as necessary, and the generated matrix is again the NFA conversion result. By repeatedly storing the data in the matrix storage unit (32 in FIG. 1), NFA conversion means (21 in FIG. 1) for converting the NFA into the specified number of simultaneously processed characters and the converted NFA description matrix are stored. An NFA conversion result matrix storage unit (32 in FIG. 1) and a result output means (22 in FIG. 1) for outputting the converted NFA.
The finite automaton generation system according to the second aspect of the present invention includes an NFA description matrix storage unit (31 in FIG. 6) that stores in advance a matrix describing an NFA of one-character transition, and an NFA description matrix after conversion. An NFA conversion result matrix storage unit (32 in FIG. 6), an NFA conversion means (23 in FIG. 6), and a result output means (22 in FIG. 6) are stored, and an NFA conversion means (23 in FIG. 6). Reads an NFA description matrix for one-character transition or an NFA description matrix for p-character transition from the NFA description matrix storage unit (31 in FIG. 6) or the NFA conversion result matrix storage unit (32 in FIG. 6), as necessary. The NFA description matrix of k-character transition is generated by dividing these into a plurality of sub-matrices, and the generated matrix is stored again in the NFA conversion result matrix storage unit (32 in FIG. 6). Parallel processing statement To generate a number of NFA.
A finite automaton generation system according to a third aspect of the present invention is an NFA description matrix that divides a matrix describing a finite automaton stored in the NFA description matrix storage unit (31 in FIG. 9) into a plurality of sub-matrices. Dividing means (24 in FIG. 9), NFA converting means (25 in FIG. 9) for performing conversion for increasing the number of characters of the transition condition of the original finite automaton using the plurality of divided partial matrices, and the NFA An NFA conversion result matrix storage unit (32 in FIG. 9) for storing a finite automaton description matrix being converted by the conversion means, and an NFA conversion result for storing a plurality of partial matrices of the finite automaton description matrix being converted by the NFA conversion means A submatrix storage unit (33 in FIG. 9) and a finite automaton description matrix in which the number of characters in the transition condition is increased to an arbitrarily designated number of characters is output. Result output means (22 in FIG. 9).
The first to third finite automaton generation systems according to the present invention adopt such a configuration and convert the NFA description matrix of one-character transition by matrix operation, thereby solving the first to third problems. be able to.

  The finite automaton generation system according to the fourth aspect of the present invention includes an NFA description matrix that generates an NFA description matrix from an input regular expression in addition to the configuration of the first, second, or third finite automaton generation system. It has a generating means (26 in FIG. 12). By adopting such a configuration, even if the NFA description matrix for one character transition is not obtained in advance, if it is a search target that can construct an NFA that transitions by one character, the NFA is generated, thereby performing simultaneous parallel processing. It can be converted to NFA of characters. The reference numerals in the drawings in the parentheses are for the purpose of making the correspondence between the present invention, the embodiment and the configuration easier to understand, and of course are not for limiting the present invention.

  A first effect is that a one-character transition finite automaton stored in advance can be converted into a finite automaton that can be used in a character string search by simultaneous parallel processing of a plurality of characters.

  The reason is that, by describing a finite automaton with one character transition in a predetermined matrix, the NFA conversion means converts the finite automaton having a transition condition with the number of characters to be subjected to simultaneous parallel processing into an NFA conversion result matrix storage unit. It is for memorizing.

  The second effect is that the conversion process is facilitated by describing a finite automaton with one character transition by a predetermined matrix, and the same process can always be performed.

  This is because a finite automaton with one character transition can be described in a matrix including its initial state and end state, and matrix operation can be performed by the NFA conversion means. In addition, since conversion using the characteristics of matrix operation is performed by the NFA conversion means, it is not necessary to repeat the processing sequentially until it can be converted into a finite automaton having a transition condition with the number of characters for which the desired simultaneous parallel processing is performed. It is.

  The third effect is that the restriction on the search target that can be converted is greatly eliminated, and if the search target can generate a one-character transition finite automaton such as a regular expression, the transition condition with the number of characters for which the desired simultaneous parallel processing is always performed. It can be converted to a finite automaton with.

  The reason is that the NFA description matrix generation means can always convert a regular expression to an NFA with a single character transition, and the NFA conversion means for conversion is described as a matrix without considering the regular expression to be searched. This is because conversion is performed on a finite automaton.

The block diagram which shows the structure of the 1st Embodiment of this invention The flowchart which shows the operation | movement of the 1st Embodiment of this invention. The figure for demonstrating the NFA description matrix of 1 character transition of this invention The flowchart which shows step A3 in the flowchart which shows the operation | movement of the 1st Embodiment of this invention. The figure for demonstrating the NFA description matrix of 4 character transition of this invention The block diagram which shows the structure of the 2nd Embodiment of this invention. The flowchart which shows the operation | movement of the 2nd Embodiment of this invention. The flowchart which shows step A6 in the flowchart which shows the operation | movement of the 2nd Embodiment of this invention. The block diagram which shows the structure of the 3rd Embodiment of this invention. The flowchart which shows the operation | movement of the 3rd Embodiment of this invention. The flowchart which shows step A9 in the flowchart which shows the operation | movement of the 3rd Embodiment of this invention. The block diagram which shows the structure of the 4th Embodiment of this invention. The flowchart which shows the operation | movement of the 4th Embodiment of this invention.

Explanation of symbols

DESCRIPTION OF SYMBOLS 1 Input device 2 Data processing device 3 Storage device 4 Output device 5 Data processing device 6 Data processing device 7 Storage device 8 Data processing device 21 NFA conversion means 22 Result output means 23 NFA conversion means 24 NFA description matrix division means 25 NFA conversion means 26 NFA description matrix generating means 31 NFA description matrix storage unit 32 NFA conversion result matrix storage unit 33 NFA conversion result submatrix storage unit A1 NFA description matrix for m character transition M _m generation preparation step A2 Convert to NFA of m characters for simultaneous parallel processing step A3 k character transition NFA description matrix conversion step A4 NFA description matrix of step A6 k character transition for outputting the step A5 results shaping the NFA description matrix of simultaneous parallel processing number m M _k to M _k to check or not Step A7 for converting the NFA description matrix S into sub-matrices -Up A8 m characters NFA description matrix M _m generation preparation step A9 k characters NFA description matrix conversion step A10 Step B2 NFA description increase the production steps B1 k from the regular expression to NFA description matrix S to M _k of the transition of the transition matrix M _kp, step B7 submatrix calculating step B6 M _k submatrix seeking step B5 submatrix to check the calculation of step B4 M _k to calculate the step B3 M _k to read M _p is complete Step B8 of calculating the sum _Mk and reading the NFA description matrices M _kp and M _p and their sub-matrices

  Next, embodiments of the present invention will be described in detail with reference to the drawings.

  FIG. 1 is a block diagram showing the configuration of the first embodiment for carrying out the present invention.

  Referring to FIG. 1, the first embodiment of the present invention includes an input device 1 such as a keyboard, a data processing device 2 that operates under program control, a storage device 3 that stores information, a display device, and a printing device. And the like.

  The storage device 3 includes an NFA description matrix storage unit 31 and an NFA conversion result matrix storage unit 32.

  The NFA description matrix storage unit 31 stores in advance a one-character transition NFA constructed from regular expressions or the like in the form of an NFA description matrix S.

The NFA conversion result matrix storage unit 32 stores an NFA description matrix M _k of k character transitions converted from the NFA description matrix S of one character transition in the NFA conversion means.

  The data processing device 2 includes an NFA conversion unit 21 and a result output unit 22.

The NFA conversion means 21 receives the NFA description matrix S for single character transition or the NFA description matrix M _p for p character transition from the NFA description matrix storage unit 31 or the NFA conversion result matrix storage unit 32 as required. The NFA description matrix M _k of k character transition is generated by using the read data, and the generated matrix M _k is stored in the NFA conversion result matrix storage unit 32 again. Such processing is repeated until an NFA description matrix M _m of m character transitions is generated according to the value of the number m of simultaneous parallel processing characters input from the input device 1.

  The result output means 22 reads the NFA description matrix of m character transitions from the NFA conversion result matrix storage unit 32, converts the NFA description matrix or the state transition diagram into a state transition diagram, and outputs it to the output device 4. It goes without saying that the NFA conversion means 21 and the result output means 22 may realize their processing and functions by a program executed on the data processing device 2.

  Next, the operation of the first embodiment for carrying out the present invention will be described in detail with reference to FIG. 1 and FIG.

The number m of simultaneous parallel processing characters given from the input device 1 is supplied to the NFA conversion means 21. The NFA converting means 21 first sets the variable k to 1 and the NFA description matrix S of one character transition read from the NFA description matrix storage unit 31 as a matrix in preparation for generating the target m character transition NFA description matrix M _m. M ₁ is stored, and the matrix M ₁ is stored in the NFA conversion result matrix storage unit 32 (step A1).

Here, an NFA description matrix S = {s _ij } (i = 1,..., N, j = 1,..., N) for a one-character transition for an NFA having n states, an NFA description matrix M for a k-character transition _k = {mk _ij } (i = 1,..., n, j = 1,..., n) will be described below. First, a row i (i = 1,..., N) or a column i (i = 1,..., N) of the NFA description matrix is associated with one of n states of the NFA, and each element s _ij and mk _ij represent characters or a set of character strings that are transition conditions from the state associated with row i and column i to the state associated with row j and column j. At this time, “+” is used to represent a plurality of conditions, and “*” is used below as a symbol representing an arbitrary character.

Furthermore, if the state associated with row i or column i is the initial state, i _s is assigned to element s _ii, and if the state associated with row i or column i is the end state , Element s _ii has f _s . For example, an NFA having the state 0 to the state 4 as shown in FIG. 3 is constructed as the NFA of the regular expression “a (bc) * (d | e)”, and the state i (i = 0,. When associated with +1, the description matrix S is expressed as [Equation 1].

[Formula 1]

  When the above-described processing (step A1) is performed by the NFA converting means 21, the size of the variable k and the number m of simultaneous parallel processing characters is subsequently compared (step A2). If the number m of simultaneously parallel processed characters is larger than the variable k, it is determined that conversion to NFA of the target m character transition has not been performed yet, and conversion processing of k character transition to NFA is performed (step A3).

FIG. 4 shows a more detailed flowchart of the operation in step A3. In step A3, the NFA converting means 21 first increases the variable k (step B1). As an increase method, if the variable k × 2 is equal to or less than the number m of simultaneous parallel processing characters, k = k × 2, otherwise k = k + 1. Subsequently, the already stored NFA description matrices M _kp and M _p are read from the NFA conversion result matrix storage unit 32 (step B2).

Here, the variable p is an integer greater than or equal to 1 and smaller than k, and M _kp and M _{p to be} read are not limited as long as their matrices have already been calculated. Using these matrices, an NFA description matrix M _k for k-character transition is calculated by taking the product of the matrices M _kp and M _p . In this calculation, the following definition is provided, and the calculation is performed according to this definition.

When a and b are characters or character strings including i _s and f _s and 0 is an empty set, they are defined as follows in the calculation of each element.

[Definition 1]: a x b = ab ≠ ba
[Definition 2]: a × 0 = 0 × a = 0
[Definition 3]: i _s × a = i _s a, a × i _s = 0, i _s × i _s = i _s i _s
[Definition _{4]: a × f s =} af s, f s × a = 0, f s × f s = f s f s

M ₂ = M ₁ × M ₁ = {m2 _ij } (i = 1,..., 5, j = 1,..., 5, k, using the NFA description matrix S = M ₁ of the one-character transition of [Formula 1] = 2, p = 1)), for example, the element m2 ₁₅ is obtained by [Expression 2].

[Formula 2]

Similarly to the above, when each element of M ₂ is calculated and it is determined that the calculation of all elements has been completed (step B4), M ₂ is calculated as in [Equation 3], and the NFA converting means 21 Stores the two-character transition NFA description matrix M ₂ in the NFA conversion result matrix storage unit 32.

[Formula 3]

Further, assuming that the number m of simultaneous parallel processing characters is 4, in order to calculate the NFA description matrix M ₄ of the _4- character transition, M ₄ = M ₂ × M using the NFA description matrix M ₂ of the 2-character transition. ₂ is calculated (k = 4, p = 2), and an NFA description matrix M ₄ of four-character transition shown in [Equation 4] can be obtained.

[Formula 4]

The NFA converting means 21, to obtain up to NFA description matrix of m characters transition object (step A2), it performs shaping of the resulting matrix M _m (step A4). Here, i _s and f _s existing in each element of the matrix are replaced with “*” representing an arbitrary character. As a result, for example, the NFA description matrix M ₄ of 4 character transition shown in [Expression 4] is shaped as [Expression 5].

[Formula 5]

When the NFA conversion unit 21 obtains the NFA description matrix M _m of the target m character transition, the NFA conversion unit 21 notifies the result output unit 22 that the result has been obtained, and the result output unit 22 stores the MFA from the NFA conversion result matrix storage unit 32. Read _m and output the result through the output device 4. At this time, the result output unit 22, an output form provides a matrix form if NFA description matrix, the NFA description matrix M _m create and output device state transition diagram of four if NFA. For example, the state transition diagram of the NFA description matrix M ₄ of the four character transition shown in [Formula 5] is as shown in FIG. However, the transition condition “****” from state 0 to state 0 and from state 4 to state 4 means an arbitrary character string in the initial state and the end state, and such an input character string does not make sense. For this reason, it is not shown in the figure. In this way, the matrix calculation processing shown in Expressions 2 to 5 is performed according to the predetermined calculation rules shown in [Definition 1] to [Definition 4].

In the first embodiment, by using a matrix for NFA conversion, conversion to NFA with simultaneous parallel processing character number transition can be performed without changing the number of original NFA states with one character transition. Furthermore, by storing only the matrix of the intermediate result of NFA conversion in the NFA conversion result matrix storage unit 32, it is possible to perform NFA conversion with a small storage capacity. In addition, by increasing k by the current k character transition NFA description matrix k and the number of simultaneous parallel processing characters m during conversion, k character transitions are sequentially increased until k reaches the number of simultaneous parallel processing characters. There is no need to calculate the NFA description matrix, and since the NFA description matrix with m-character transition is finally formatted, “*” representing an arbitrary character is generated from either i _s or f _s Judgment becomes unnecessary. Therefore, processing related to matrix calculation is simplified, and the generation speed can be improved.

  In the above embodiment, the method of increasing the variable k is determined by comparison with the number m of simultaneous parallel processing, but a method of increasing the variable k by always setting k = k + 1 may be used.

  In addition to the nondeterministic finite automaton (NFA), the same configuration as that of the present embodiment can be applied to the deterministic finite automaton (DFA).

  Next, a second embodiment for carrying out the present invention will be described in detail with reference to the drawings.

  FIG. 6 is a block diagram showing the configuration of the second embodiment for carrying out the present invention.

  Referring to FIG. 6, the data processing apparatus 5 according to the second embodiment of the present invention is the same as that of the data processing apparatus 2 in the first embodiment shown in FIG. The conversion means 23 is replaced. Other points are the same as those in the first embodiment.

  The data processing device 5 includes an NFA conversion unit 23 and a result output unit 22.

The NFA conversion means 23 receives the NFA description matrix S for single character transition or the NFA description matrix M _p for p character transition from the NFA description matrix storage unit 31 or the NFA conversion result matrix storage unit 32 as required. Read, divide them into three sub-matrices to generate an NFA description matrix M _k with k-character transition, and store the generated matrix M _k in the NFA conversion result matrix storage unit 32 again. Here, as three divided matrices, the partial matrix of the first character transition NFA description matrix S S to ', Si, Sa, NFA description matrix M _k to M k-character transition' _k, Mi _k, and Ma _k. Such processing is repeated according to the value of the number m of simultaneously processed parallel characters input from the input device 1 until an NFA of m character transitions is generated. Since the result output means 22 is the same as that of the first embodiment, description thereof is omitted. It goes without saying that the NFA conversion means 23 and the result output means 22 may realize their processing and functions by a program executed on the data processing device 5.

  Next, the operation of the second embodiment for carrying out the present invention will be described in detail with reference to FIG. 6 and FIG.

The number m of simultaneous parallel processing characters given from the input device 1 is supplied to the NFA conversion means 23. First, the NFA converting means 23 sets the variable k to 1 and the 1-character transition NFA description matrix S read from the NFA description matrix storage unit 31 as a matrix in preparation for generating the target m-character transition NFA description matrix M _m. M ₁ is stored, and the matrix M ₁ is stored in the NFA conversion result matrix storage unit 32 (step A1). Since the meanings of the NFA description matrices S and M ₁ are the same as those in the first embodiment, description thereof is omitted.

  When the above-described processing (step A1) is performed by the NFA conversion means 23, the variable k and the number m of simultaneously parallel processed characters m are subsequently compared (step A2). If the number m of simultaneous parallel processing characters is larger than the variable k, it is determined that conversion to NFA of the target m character transition has not been performed yet, and conversion processing of k character transition to NFA is performed (step A6).

FIG. 8 shows a more detailed flowchart of the operation in step A6. In step A6, the NFA conversion means 23 first increases the variable k (step B1), and reads out the already stored NFA description matrices M _kp and M _p from the NFA conversion result matrix storage unit 32 (step B2). . Since these methods are the same as those in the first embodiment, description thereof is omitted.

Subsequently, from these matrices M _kp and M _p, each subarray _{M 'kp, Mi kp, Ma} kp, M' p, Mi p, seek Ma _p (step B5).

Here, NFA description matrix Mk submatrix M _'k of k characters transition, Mi _k, the Ma _k is defined as follows. First, the sub-matrices M ′ ₁ , Mi ₁ , and Ma ₁ of the NFA description matrix M _k = S when k = 1 are defined as follows.

[Definition 5]: The submatrix M ′ ₁ is a matrix in which each element has only elements other than i _s and f _s .

[Definition 6]: The submatrix Mi ₁ has only i _s as an element, and this i _s is replaced with “*” representing an arbitrary character.

[Definition 7]: The submatrix Ma ₁ has only f _s as an element, and this f _s is replaced with “*” representing an arbitrary character.

[Definition 8]: M ₁ = M ′ ₁ + Mi ₁ + Ma ₁

For example, when the description matrix S is expressed as [Equation 1], M ′ ₁ , Mi ₁ , Ma ₁ , and M ₁ are expressed as [Equation 6].

[Formula 6]

The partial matrix M _'k of NFA description matrix M _k where k is greater than 1, Mi _k, Ma _k is represented by the following definitions.

[Definition 9]: The submatrix M ′ _k is a matrix in which each element does not have “*” at the end. In other words, there can be elements like “** a…”, but there are no elements like “… a **”.

[Definition 10]: submatrix Mi _k has only elements such as the product of a "** ..." replaced "*" from the i _s indicating the initial state to the element both.

[Definition 11]: The sub-matrix Ma _k is a matrix composed of only elements having “*” at the end of each element. In other words, it has only elements such as “… a **”.

NFA converting means 23 uses the submatrices as described above, partial matrix M _'k of NFA description matrix M _k of k characters transition, Mi _k, seek Ma _k. For the calculation at this time, definitions 1 to 4 defined in the first embodiment are used. Here, when M _k = M _kp × M _p is calculated using definitions 1 to 4, [Equation 7] is obtained.

[Formula 7]

By definition 3,4, since the _{M 'kp × Mi p = 0} , Ma kp × M' p = 0, Ma kp × Mi p = 0, represented by [Equation 7] [Equation 8].

[Formula 8]

By definition 9, 10 and 11 and [Expression 8], NFA description matrix M _k submatrix M _'k of k characters transition, Mi _k, Ma _k can be defined as [Equation 9]. In the calculation of [Equation 9], “*” representing an arbitrary character is treated as a normal character and calculation is performed.

[Formula 9]

NFA converting means 23, the read and matrices M _kp and M _p from NFA conversion result matrix storage unit 32, obtains each subarray _{M 'kp, Mi kp, Ma} kp, M' p, Mi p, the Ma _p (Step B5) and M ′ _k , Mi _k , and Mak are _obtained from the above [Equation 9] (Step B6). The NFA description matrix M _k of k character transition is calculated by taking the sum of them (step B7), and when it is determined that the calculation of all the elements has been completed (step B4), the NFA conversion means 23 uses k characters. The NFA description matrix M _k of the transition is stored in the NFA conversion result matrix storage unit 32.

For example, the sub-matrix of M ₂ using the sub-matrix of the NFA description matrix S = M ₁ (Equation 6) of the one-character transition of the regular expression “a (bc) * (d | e)” shown in FIG. When the sum is obtained, [Formula 10] is obtained.

[Formula 10]

Furthermore, if concurrent parallel processing number m is set to be 4, 4 to calculate the the NFA description matrix M ₄ character transitions, using 2 character transition NFA description matrix M ₂ submatrix, calculated M ₄ (K = 4, p = 2), the sub-matrix of the 4-character transition NFA description matrix M ₄ shown in [Equation 11] and M ₄ can be obtained.

[Formula 11]

  When the NFA conversion means 23 obtains the NFA description matrix of the desired m-character transition (step A2), it notifies the result output means 22 that the result has been obtained, and the subsequent operation is the same as in the first embodiment. Therefore, the description is omitted.

  In the second embodiment, as in the first embodiment, by using a matrix for NFA conversion, the number of simultaneous parallel processing character number transitions can be changed without changing the number of NFA states of the original one-character transition. Can be converted to NFA. Further, since the definition 1 to the definition 4 are already taken into account in the matrix calculation in the NFA conversion means, it is not necessary to check each element during the calculation. For this reason, although generation of each partial matrix is required, processing such as branching is not required, and the generation speed can be improved.

  In the above embodiment, as in the first embodiment, the method for increasing the variable k is determined by comparison with the simultaneous parallel processing number m, but it may be always increased as k = k + 1. Further, not only a nondeterministic finite automaton (NFA) but also a deterministic finite automaton (DFA) can be applied in the same embodiment.

  Next, a third embodiment for carrying out the present invention will be described in detail with reference to the drawings.

  FIG. 9 is a block diagram showing the configuration of the third exemplary embodiment for carrying out the present invention.

  Referring to FIG. 9, in the data processing apparatus 6 according to the third embodiment of the present invention, in the configuration of the data processing apparatus 5 in the second embodiment shown in FIG. The conversion unit 25 is replaced with an NFA description matrix division unit 24. The storage device 7 includes an NFA conversion result submatrix storage unit 33 in the storage device 3 in the second embodiment shown in FIG. ing. The other points are the same as in the second embodiment.

  The data processing device 6 includes an NFA description matrix dividing unit 24, an NFA converting unit 25, and a result output unit 22.

  The NFA description matrix dividing means 24 reads the NFA description matrix S of one character transition from the NFA description matrix storage unit 31, divides it into partial matrices S ′, Si, Sa, and those matrices together with the NFA description matrix S of one character transition. Is provided to the NFA converting means 25.

The NFA converting means 25 converts the NFA description matrix S from the NFA description matrix dividing means 24 and its partial matrices S ′, Si, Sa into an NFA description matrix M ₁ of one-character transition and its partial matrices M ′ ₁ , Mi ₁ , Ma ₁ , and M ₁ is stored in the NFA conversion result matrix storage unit 32, and the partial matrices M ′ ₁ , Mi ₁ , and Ma ₁ are stored in the NFA conversion result submatrix storage unit 33. The NFA conversion means 25 converts the _KFA character transition NFA description matrix M _kp and its partial matrices M ′ _kp , Mi _kp already converted and stored in the NFA conversion result matrix storage unit 32 and the NFA conversion result submatrix storage unit 33. , Ma _kp also,, NFA description matrix of p character transition M _p and its partial matrix M _'p, Mi _p, read as needed Ma _p, part of the NFA description matrix M _k of k characters transitions with them matrix M _'k, Mi _k, generates Ma _k, generates a M _k by taking their sum, they generated their matrix again NFA conversion result matrix storage unit 32, NFA conversion result sub-matrix storage unit 33 Remember me. Here, the meanings of the various matrices and the result output means 22 are the same as those in the second embodiment, and a description thereof will be omitted.

  The storage device 7 includes an NFA description matrix storage unit 31, an NFA conversion result matrix storage unit 32, and an NFA conversion result submatrix storage unit 33.

NFA conversion result sub-matrix storage unit 33 is a submatrix of the NFA description matrix M _k of k characters transitions M _'k, Mi _k, stores Ma _k. Since the NFA description matrix storage unit 31 and the NFA conversion result matrix storage unit 32 are the same as those in the second embodiment, description thereof will be omitted. In the present embodiment, the NFA description matrix dividing unit 24, the NFA converting unit 25, and the result output unit 22 may realize their processing and functions by a program executed on the data processing device 6. Of course.

  Next, the operation of the third embodiment for carrying out the present invention will be described in detail with reference to FIG. 9 and FIG.

The number m of simultaneous parallel processing characters given from the input device 1 is supplied to the NFA conversion means 25. The NFA description matrix dividing means 24 divides the NFA description matrix S of one character transition read from the NFA description matrix storage unit 31 into partial matrices S ′, Si, Sa (step A7). The NFA description matrix dividing unit 24 provides these matrices to the NFA converting unit 25, and the NFA converting unit 25 converts each of the matrices received from the NFA description matrix dividing unit 24 into an NFA description matrix M ₁ of one character transition, and 'a _1, Mi _1, Ma _1, the M ₁ to NFA conversion result matrix storage unit 32, the partial matrix M' the sub-matrix M to store _1, Mi _1, Ma ₁ to NFA conversion result sub-matrix storage unit 33 (Step A8).

Note that the meanings of the NFA description matrices S and M _{1 and} the meanings of these sub-matrices are the same as those in the second embodiment, and thus description thereof is omitted.

  When the above-described processing (step A8) is performed by the NFA conversion means 25, the variable k and the number m of simultaneously parallel processed characters m are subsequently compared (step A2). If the number m of simultaneous parallel processing characters is larger than the variable k, it is determined that conversion to NFA of the target m character transition has not been performed yet, and conversion processing of k character transition to NFA is performed (step A9).

FIG. 11 shows a more detailed flowchart of the operation in step A9. In step A9, the NFA conversion means 25 first increases the variable k (step B1), and the NFA description matrix M _kp and M _p already stored from the NFA conversion result matrix storage unit 32 are used as the NFA conversion result submatrix. from the storage unit 33, reads NFA submatrix M of description matrix M _kp and _{M p 'kp, Mi kp,} Ma kp, M' p, Mi p, the Ma _p (step B8). The subsequent operation, as well as to store the NFA description matrix M _k of the calculated k character transitions in NFA conversion result matrix storage unit 32, the partial matrix M _'k, Mi _k, Ma _k the NFA conversion result sub-matrix Since it is the same as that of 2nd Embodiment except memorize | storing in the memory | storage part 33, description is abbreviate | omitted.

In the above-described third embodiment, the matrix operation in NFA converting means, not only the NFA description matrix M _k the converted k character transition, the partial matrix M _'k, Mi _k, Ma _k also NFA conversion result part Since the data is stored in the matrix storage unit 33, it is not necessary to divide the matrix into sub-matrices every time the NFA conversion unit repeats conversion. For this reason, the generation speed of the NFA description matrix of k character transition can be improved.

  In the above embodiment, as in the first and second embodiments, the method for increasing the variable k is determined by comparison with the simultaneous parallel processing number m. However, even if it is always increased as k = k + 1. good. Further, not only a nondeterministic finite automaton (NFA) but also a deterministic finite automaton (DFA) can be applied in the same embodiment.

  Next, a fourth embodiment for carrying out the present invention will be described in detail with reference to the drawings.

  FIG. 12 is a block diagram showing the configuration of the fourth embodiment for carrying out the present invention.

  Referring to FIG. 12, the data processing apparatus 8 according to the fourth embodiment of the present invention has an NFA description matrix generating means 26 in the configuration of the data processing apparatus 6 in the third embodiment shown in FIG. The other points are the same as those of the third embodiment.

  The data processing apparatus 8 includes an NFA description matrix generation unit 26, an NFA description matrix division unit 24, an NFA conversion unit 25, and a result output unit 22.

  The NFA description matrix generating means 26 is provided with the regular expression itself from the input device 1. When provided with a regular expression, the NFA description matrix generation means 26 constructs a syntax tree from the regular expression and generates an NFA of one-character transition from the syntax tree. An NFA description matrix S is generated from the generated NFA and stored in the NFA description matrix storage unit 31. In this embodiment, the NFA description matrix generation means 26, the NFA description matrix division means 24, the NFA conversion means 25, and the result output means 22 realize their processing and functions by a program executed on the data processing device 8. Of course, you may make it do.

  Next, the operation of the fourth embodiment for carrying out the present invention will be described in detail with reference to FIGS.

  The number m of simultaneous parallel processing characters given from the input device 1 is supplied to the NFA conversion means 25. Further, the regular expression itself is supplied from the input device 1 to the NFA description matrix generation means 26. A syntax tree is constructed based on a regular expression as described in [Non-Patent Document 1], and an NFA of one-character transition is generated from the syntax tree. In general, in the method of constructing an NFA from a regular expression using such a method, there is a list that holds the transition destination state from each state and its transition condition, so an NFA description matrix S is generated from the list. Then, it is stored in the NFA description matrix storage unit 31 (step A10). Since the subsequent processing is the same as that of the third embodiment, detailed description thereof is omitted.

  In the fourth embodiment, when an NFA description matrix is not stored in the NFA description matrix storage unit 31 in advance, an NFA is constructed using an existing NFA construction method by inputting a regular expression. An NFA description matrix S can be generated. For this reason, it is possible to generate an NFA description matrix that transitions by the number of simultaneously processed parallel characters using a regular expression that is flexibly given.

  The fourth embodiment is a form in which the NFA description matrix generation means 26 is provided in the configuration of the third embodiment, but also in the first embodiment and the second embodiment. By providing the same NFA description matrix generation means 26, it is possible to generate an NFA description matrix that transitions with a specified number of simultaneously processed characters from a given regular expression.

  In the first to fourth embodiments, each unit of the processing device and the storage device is configured by hardware. However, a part or all of each unit can be caused to function as a program in the information processing apparatus.

As an example of use of the present invention, pattern matching processing of attack / intrusion rules in an intrusion detection system (IDS: Intrusion Detection System) and intrusion prevention system (IPS: Intrusion Prevention System) for detecting attacks and intrusions on network services is realized at high speed. It can be applied to a use such as a program for generating an automaton for the purpose. It can also be applied to automaton generation in software-based pattern matching processing installed in personal computers and workstations.
Within the scope of the entire disclosure (including claims) of the present invention, the embodiments and examples can be changed and adjusted based on the basic technical concept. Various combinations and selections of various disclosed elements are possible within the scope of the claims of the present invention. That is, the present invention of course includes various variations and modifications that could be made by those skilled in the art according to the entire disclosure including the claims and the technical idea.

Claims (42)

  A finite automaton generation system comprising means for increasing the number of characters of a transition condition of a finite automaton composed of transition conditions of a fixed number of characters to an arbitrarily designated number of characters.   The finite automaton generation system according to claim 1, wherein the finite automaton is described in a matrix format.   The finite automaton generation system according to claim 1 or 2, wherein the increasing means does not change the number of states of the original finite automaton.   4. The finite automaton generation system according to claim 2, wherein the increasing means is configured to follow a matrix operation having a predetermined operation rule.   4. The finite automaton generation system according to claim 2, wherein the increasing means is configured to apply a predetermined operation rule to a matrix operation using a plurality of sub-matrices. .   6. The finite automaton generation system according to claim 5, wherein the matrix calculation using the plurality of partial matrices generates and uses a partial matrix every time the calculation is performed.   6. The finite automaton generation system according to claim 5, wherein the matrix operation using the plurality of partial matrices generates a partial matrix in advance and uses the partial matrix. NFA description matrix storage means for storing a finite automaton having a transition condition of a fixed number of characters previously described in the form of a matrix;
NFA conversion means for performing conversion for increasing the number of characters of the transition condition of the finite automaton described by the matrix stored in the NFA description matrix storage means;
NFA conversion result matrix storage means for storing a finite automaton description matrix being converted by the NFA conversion means;
A finite automaton generation system comprising: a result output unit that outputs a finite automaton in which the number of characters of the transition condition is increased to an arbitrarily designated number of characters.   The NFA conversion means reads a finite automaton description matrix of one character transition or a finite automaton description matrix of p character transition from the NFA description matrix storage means or the NFA conversion result matrix storage means, respectively, and the read finite automaton description matrix Is divided into a plurality of sub-matrices to generate a k-character transition finite automaton description matrix, and the process of storing the generated k-character transition finite automaton description matrix in the NFA conversion result matrix storage means is repeated. 9. The finite automaton generation system according to claim 8, wherein a finite automaton having the number of simultaneously processed parallel characters is generated. NFA description matrix storage means for storing a finite automaton having a transition condition of a fixed number of characters previously described in the form of a matrix;
NFA description matrix dividing means for dividing the matrix describing the finite automaton stored in the NFA description matrix storage means into a plurality of partial matrices;
NFA conversion means for performing conversion for increasing the number of characters of the transition condition of the original finite automaton using the plurality of divided sub-matrices;
NFA conversion result matrix storage means for storing a finite automaton description matrix being converted by the NFA conversion means;
NFA conversion result partial matrix storage means for storing a plurality of partial matrices of a finite automaton description matrix being converted by the NFA conversion means;
A finite automaton generation system comprising: a result output unit that outputs a finite automaton in which the number of characters of the transition condition is increased to an arbitrarily designated number of characters.   The means for increasing converts the input regular expression into a finite automaton having a transition condition of one character, and arbitrarily increases the number of characters in the transition condition of the converted finite automaton. The finite automaton generation system according to claim 3. NFA description matrix generating means for converting the input regular expression into a matrix describing a finite automaton having a one-character transition condition;
NFA description matrix storage means for storing the matrix after conversion by the NFA description matrix generation means;
NFA conversion means for performing conversion for increasing the number of characters of the transition condition of the finite automaton described by the matrix stored in the NFA description matrix storage means;
NFA conversion result matrix storage means for storing a finite automaton description matrix being converted by the NFA conversion means;
A finite automaton generation system comprising: a result output unit that outputs a finite automaton in which the number of characters of the transition condition is increased to an arbitrarily designated number of characters. NFA description matrix generating means for converting the input regular expression into a matrix describing a finite automaton having a one-character transition condition;
NFA description matrix storage means for storing the matrix after conversion by the NFA description matrix generation means;
NFA description matrix dividing means for dividing a matrix describing the finite automaton stored in the NFA description matrix storage means into a plurality of partial matrices;
NFA conversion means for performing conversion for increasing the number of characters of the transition condition of the original finite automaton using the plurality of divided sub-matrices;
NFA conversion result matrix storage means for storing a finite automaton description matrix being converted by the NFA conversion means;
NFA conversion result partial matrix storage means for storing a plurality of partial matrices of a finite automaton description matrix being converted by the NFA conversion means;
A finite automaton generation system comprising: a result output unit that outputs a finite automaton in which the number of characters of the transition condition is increased to an arbitrarily designated number of characters.   14. The result output means outputs the finite automaton increased to the arbitrarily designated number of characters in a matrix form and / or a state transition diagram. A finite automaton generation system according to claim 1.   A method for generating a finite automaton, wherein the number of characters in a transition condition of a finite automaton composed of transition conditions of a fixed number of characters is increased to an arbitrarily designated number of characters.   The finite automaton generation method according to claim 15, wherein the finite automaton is described in a matrix format.   The finite automaton generation method according to claim 15 or 16, wherein the number of states of the original finite automaton is not changed.   18. The method of generating a finite automaton according to claim 16, wherein the number of characters of the transition condition of the finite automaton is increased according to a matrix operation having a predefined operation rule.   18. The finite automaton generation according to claim 16 or 17, wherein the number of characters of the transition condition of the finite automaton is increased by applying a predefined operation rule to a matrix operation using a plurality of sub-matrices. Method.   The finite automaton generation method according to claim 19, wherein the matrix operation using the plurality of submatrices generates and uses a submatrix every time the operation is performed.   The finite automaton generation method according to claim 19, wherein the matrix calculation using the plurality of partial matrices generates a partial matrix in advance and uses the partial matrix. Store a finite automaton having a transition condition of a fixed number of characters described in advance in the form of a matrix,
Performing a conversion to increase the number of characters of the transition condition of the finite automaton described by the stored matrix,
Memorize the finite automaton description matrix in the middle of conversion,
A finite automaton generation method comprising outputting a finite automaton in which the number of characters of the transition condition is increased to an arbitrarily designated number of characters.   Read a finite automaton description matrix of one character transition or a p character transition finite automaton description matrix stored in advance, and divide the read finite automaton description matrix into a plurality of sub-matrices to obtain a k character transition finite automaton description matrix. 23. The finite automaton generation according to claim 22, wherein a finite automaton having a specified number of simultaneously processed characters is generated by repeating the process of generating and storing the generated finite automaton description matrix of the k character transition. Method. Store a finite automaton having a transition condition of a fixed number of characters described in advance in the form of a matrix,
Dividing the matrix describing the stored finite automaton into a plurality of sub-matrices;
Performing conversion to increase the number of characters of the transition condition of the original finite automaton using the plurality of divided sub-matrices,
Memorize the finite automaton description matrix in the middle of conversion,
Memorize multiple sub-matrices of finite automaton description matrix in the middle of conversion,
A finite automaton generation method comprising outputting a finite automaton in which the number of characters of the transition condition is increased to an arbitrarily designated number of characters. Convert the input regular expression into a finite automaton with a one-character transition condition,
The finite automaton generation method according to any one of claims 15 to 17, wherein the number of characters in the transition condition of the converted finite automaton is arbitrarily increased. Convert the input regular expression into a matrix describing a finite automaton with a one-character transition condition,
Remember the transformed matrix,
Performing a conversion to increase the number of characters of the transition condition of the finite automaton described by the stored matrix,
Memorize the finite automaton description matrix in the middle of conversion,
A finite automaton generation method comprising outputting a finite automaton in which the number of characters of the transition condition is increased to an arbitrarily designated number of characters. Convert the input regular expression into a matrix describing a finite automaton with a one-character transition condition,
Remember the transformed matrix,
Dividing the transformed matrix into a plurality of sub-matrices;
Using the plurality of divided sub-matrices, performing a conversion to increase the number of characters of the transition condition of the original finite automaton,
Memorize the finite automaton description matrix in the middle of conversion,
Memorize multiple sub-matrices of finite automaton description matrix in the middle of conversion,
A finite automaton generation method comprising outputting a finite automaton in which the number of characters of the transition condition is increased to an arbitrarily designated number of characters.   The finite automaton increased to the arbitrarily specified number of characters is output in a matrix format and / or a state transition diagram, and the finite number according to any one of claims 22, 23, 24, 26, and 27. Automaton generation method.   A finite automaton generation program that causes a computer to execute a process of increasing the number of characters of a transition condition of a finite automaton composed of transition conditions of a fixed number of characters to an arbitrarily designated number of characters.   30. The finite automaton generation program according to claim 29, wherein the finite automaton is described in a matrix format.   The finite automaton generation program according to claim 29 or 30, wherein, in the increasing process, the number of states of the original finite automaton is not changed.   32. The finite automaton generation program according to claim 30, wherein, in the increasing process, the computer executes a matrix operation process having a predetermined operation rule.   32. The finite automaton generation program according to claim 30, wherein, in the increasing process, a computer is caused to execute a process of applying a predetermined operation rule to a matrix operation using a plurality of partial matrices. .   34. The finite automaton generation program according to claim 33, wherein the matrix calculation using the plurality of partial matrices generates and uses a partial matrix each time the calculation is performed.   34. The finite automaton generation program according to claim 33, wherein the matrix calculation using the plurality of partial matrices generates a partial matrix in advance and uses the partial matrix. An NFA description matrix storage process for storing a finite automaton having a transition condition of a fixed number of characters previously described in a matrix format;
NFA conversion processing for performing conversion to increase the number of characters of the transition condition of the finite automaton described by the matrix stored by the NFA description matrix storage processing;
An NFA conversion result matrix storage process for storing a finite automaton description matrix in the middle of conversion by the NFA conversion process;
A finite automaton generation program that causes a computer to execute a result output process for outputting a finite automaton in which the number of characters in the transition condition is increased to an arbitrarily designated number of characters.   The NFA conversion process reads out the one-character transition finite automaton description matrix or p-character transition finite automaton description matrix stored in the NFA description matrix storage process or the NFA conversion result matrix storage process, respectively, and reads the read finite By dividing the automaton description matrix into a plurality of sub-matrices and generating a finite automaton description matrix of k-character transitions, and repeating the process of storing the generated finite automaton description matrix of k-character transitions, the specified simultaneous parallel processing The finite automaton generation program according to claim 36, wherein a finite automaton having a number of characters is generated. An NFA description matrix storage process for storing a finite automaton having a transition condition of a fixed number of characters previously described in a matrix format;
An NFA description matrix dividing process for dividing the stored finite automaton description matrix into a plurality of sub-matrices;
NFA conversion processing for performing conversion to increase the number of characters of the transition condition of the original finite automaton using the plurality of divided sub-matrices;
An NFA conversion result matrix storage process for storing a finite automaton description matrix in the middle of conversion by the NFA conversion process;
NFA conversion result partial matrix storage processing for storing a plurality of partial matrices of a finite automaton description matrix being converted by the NFA conversion processing;
A finite automaton generation program that causes a computer to execute a result output process for outputting a finite automaton in which the number of characters in the transition condition is increased to an arbitrarily designated number of characters. In the increasing process, the input regular expression is converted into a finite automaton having a one-character transition condition;
32. The finite automaton generation program according to claim 29, further causing a computer to execute a process of arbitrarily increasing the number of characters of the converted finite automaton transition condition. An NFA description matrix generation process for converting the input regular expression into a matrix describing a finite automaton having a transition condition of one character;
An NFA description matrix storage process for storing a matrix after conversion by the NFA description matrix generation process;
NFA conversion processing for performing conversion to increase the number of characters of the transition condition of the finite automaton described by the matrix stored by the NFA description matrix storage processing;
An NFA conversion result matrix storage process for storing a finite automaton description matrix in the middle of conversion by the NFA conversion process;
A finite automaton generation program that causes a computer to execute a result output process for outputting a finite automaton in which the number of characters in the transition condition is increased to an arbitrarily designated number of characters. An NFA description matrix generation process for converting the input regular expression into a matrix describing a finite automaton having a transition condition of one character;
An NFA description matrix storage process for storing a matrix after conversion by the NFA description matrix generation process;
An NFA description matrix division process for dividing a matrix describing a finite automaton stored by the NFA description matrix storage process into a plurality of sub-matrices;
NFA conversion processing for performing conversion to increase the number of characters of the transition condition of the original finite automaton using the plurality of divided sub-matrices;
An NFA conversion result matrix storage process for storing a finite automaton description matrix in the middle of conversion by the NFA conversion process;
NFA conversion result partial matrix storage processing for storing a plurality of partial matrices of a finite automaton description matrix being converted by the NFA conversion processing;
A finite automaton generation program that causes a computer to execute a result output process for outputting a finite automaton in which the number of characters in the transition condition is increased to an arbitrarily designated number of characters.   42. The result output process outputs the finite automaton increased to the arbitrarily designated number of characters in a matrix format and / or a state transition diagram, wherein any one of claims 36, 37, 38, 40 and 41 is provided. A finite automaton generation program according to any one of the above.

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